Fundamentals of Mathematics XI

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Book Details:

• Authors: Parmanand Gupta, Prafulla Kumar Sahoo

• ISBN: 9789357677639

• Edition: New 2023

• Pages: 842

About the Book:
This book is designed as both a textbook and a supplement to standard texts for the prescribed course. It aligns with the latest syllabus prescribed by the Council of Higher Secondary Education (CHSE). The subject matter in each chapter has been thoroughly revised, ensuring it reflects the mark allocation of the current syllabus. Each chapter begins with a clear explanation of relevant definitions, principles, and theorems, along with illustrative and descriptive material. At the end of each chapter, a summary of important formulae is provided.

The book includes numerous solved problems to explain and amplify theoretical concepts, focusing on key points essential for students' understanding. A significant number of unsolved problems with answers serve as a comprehensive revision tool. A new feature, Working Rules/Steps for Solving Problems, has been introduced to help students tackle various types of problems more confidently. The more challenging problems come with hints to guide students, ensuring they are not discouraged by overly complex exercises, which are not expected at the +2 level.

Each exercise is divided into four parts:

• Detailed theory with clear diagrams

• Solved problems

• Unsolved problems

• Working rules/steps for solving problems before exercises

Each exercise is further divided into three groups:

• Very Short Answer / Short Answer Type Questions

• Long Answer-I Type Questions

• Long Answer-II Type Questions

The book also includes hints for tricky problems, a summary at the end of each chapter, and questions from NCERT and Exemplar Problems textbooks.

About the Authors:

• Parmanand Gupta: M.Sc. in Mathematics from Delhi University (1974), M.A. in Economics from Punjabi University, and M.Phil. in Mathematics. He has over 40 years of teaching experience and retired as Associate Professor and Head of the Mathematics Department at a degree college.

• Prafulla Kumar Sahoo: M.Sc. in Mathematics from Utkal University (1980), M.Phil. from Utkal University (1982). Currently, he serves as Reader and Head of the Mathematics Department at Christ College, Cuttack, with over 35 years of teaching experience.

Contents:

UNIT-I: Sets and Functions

1. Sets

2. Relations

3. Functions

4. Measurement of Angles

5. Trigonometric Functions

6. Graphs of Trigonometric Functions

7. Trigonometric Functions of Sum and Difference of Two Angles

8. Transformation Formulae

9. Trigonometric Functions of Multiple and Sub-multiple Angles

10. Conditional Identities

11. Trigonometric Equations

12. Sine and Cosine Formulae

UNIT-II: Algebra
13. Principle of Mathematical Induction
14. Complex Numbers
15. Quadratic Equations
16. Linear Inequalities
17. Permutations
18. Combinations
19. Binomial Theorem
20. Arithmetic Progressions
21. Geometric Progressions
22. Harmonic Progressions
23. Some Special Series
24. Arithmetico-Geometric Series
25. Binomial Series
26. Exponential Series
27. Logarithmic Series

UNIT-III: Coordinate Geometry
28. Brief Recall of Two Dimensional Coordinates
29. Straight Lines
30. Circle
31. Parabola
32. Ellipse
33. Hyperbola
34. Introduction to Three Dimensional Geometry

UNIT-IV: Calculus
35. Limits
36. Differentiation

UNIT-V: Mathematical Reasoning
37. Mathematical Reasoning

UNIT-VI: Statistics and Probability
38. Statistics
39. Probability